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<div style="margin-left: 40px;"><span lang="en-us">4.<a href="#4.ODE_solvers">ODE solvers</a></span><div style="margin-left: 40px;">
	<span lang="en-us">4.1. <a href="#4.1._Euler">Euler</a><br>4.2. 
	<a href="#4.2._Euler_Improved">Euler Improved</a><br>4.3. 
	<a href="#4.3._Runge-Kutta">Runge-Kutta</a><br><br>&nbsp;</span></div>
	<hr>
	<p><b><span lang="en-us"><a name="4.ODE_solvers">4.ODE solvers</a></span></b></p>
	<p><span lang="en-us">VISUNS has embedded 3 Ordinary differential equations 
	solvers based on Taylor expansions. This solvers only work with equations in 
	state form. Equations can be of any order and these are fix step ODE 
	solvers.</span></p>
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	<p align="right">&nbsp;</p>
	<blockquote>
		<p><b><span lang="en-us"><a name="4.1._Euler">4.1. Euler</a></span></b></p>
		<blockquote>
			<span lang="EN-US" style="font-size: 12.0pt; font-family: Times New Roman">
			<span style="position: relative; top: 6.0pt"><span lang="en-us">This 
			is a single pass solver based on first order Taylor expansions.</span></span></span><b><span lang="en-us"><br>
			<br>
			<img border="0" src="ode_archivos/euler.jpg" width="204" height="39"></span></b></blockquote>
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		<p><b><span lang="en-us"><a name="4.2._Euler_Improved">4.2. Euler Improved</a></span></b></p>
		<blockquote>
			<p><span lang="en-us">Euler Improved is a second order Runge 
			Kutta</span></p>
			<!--[if gte mso 9]><![endif]-->
			<img border="0" src="ode_archivos/improved%20euler.JPG"></blockquote>
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		<blockquote>
			<p>&nbsp;</p>
		</blockquote>
		<b><span lang="en-us"><a name="4.3._Runge-Kutta">4.3. Runge-Kutta</a></span></b><blockquote>
			<p><b><span lang="en-us"><br></span></b>
			<img border="0" src="ode_archivos/runge%20kutta.JPG"></p>
		</blockquote>
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		<p>&nbsp;</p>
	</blockquote>
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